OFFSET
1,2
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..313
Jozsef Sandor, On bi-unitary harmonic numbers, arXiv:1105.0294 [math.NT], 2011.
EXAMPLE
a(3) = 3 since A286325(3) = 45, the bi-unitary divisors of 45 are 1, 5, 9, and 45, and their harmonic mean is 3.
MATHEMATICA
f[p_, e_] := p^e * If[OddQ[e], (e + 1)*(p - 1)/(p^(e + 1) - 1), e/((p^(e + 1) - 1)/(p - 1) - p^(e/2))]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; Select[Array[s, 10^5], IntegerQ]
PROG
(PARI) bhmean(n) = {my(f = factor(n), p, e); n * prod(i = 1, #f~, p = f[i, 1]; e = f[i, 2]; if(e%2, (e + 1)*(p - 1)/(p^(e + 1) - 1), e/((p^(e + 1) - 1)/(p - 1) - p^(e/2)))); }
lista(kmax) = {my(bh); for(k = 1, kmax, bh = bhmean(k); if(denominator(bh) == 1, print1(bh, ", "))); }
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Mar 24 2023
STATUS
approved